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Circumradius of Decagon given Height Formula

GoCircumradius of Decagon given Width Formula

GoCircumradius of Decagon given Diagonal across Five Sides Formula

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Circumradius of Decagon is the radius of a circumcircle touching each of the Decagon's vertices. Check FAQs

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{h}{\sqrt{5 + (2 \cdot \sqrt{5})}}

r_c - Circumradius of Decagon?h - Height of Decagon?

Circumradius of Decagon given Height Example

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Here is how the Circumradius of Decagon given Height equation looks like with Values.

Here is how the Circumradius of Decagon given Height equation looks like with Units.

Here is how the Circumradius of Decagon given Height equation looks like.

16.2977 = \frac{1 + \sqrt{5}}{2} \cdot \frac{31}{\sqrt{5 + (2 \cdot \sqrt{5})}}

16.2977m = \frac{1 + \sqrt{5}}{2} \cdot \frac{31m}{\sqrt{5 + (2 \cdot \sqrt{5})}}

16.2977 = \frac{1 + \sqrt{5}}{2} \cdot \frac{31}{\sqrt{5 + (2 \cdot \sqrt{5})}}

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Circumradius of Decagon given Height Solution

Follow our step by step solution on how to calculate Circumradius of Decagon given Height?

FIRST Step Consider the formula

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{h}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Next Step Substitute values of Variables

∴

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{31m}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Next Step Prepare to Evaluate

∴

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{31}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Next Step Evaluate

∴

r c = 16.2976644756931m

LAST Step Rounding Answer

∴

r c = 16.2977m

Circumradius of Decagon given Height Formula Elements

Variables

Functions

Circumradius of Decagon

Circumradius of Decagon is the radius of a circumcircle touching each of the Decagon's vertices.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Decagon

Height of Decagon

Height of Decagon is the length of a perpendicular line drawn from one vertex to the opposite side.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Decagon

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Circumradius of Decagon

Go Circumradius of Decagon given Width

r c = \frac{w}{2}

Go Circumradius of Decagon given Diagonal across Five Sides

r c = \frac{d 5}{2}

Go Circumradius of Decagon given Diagonal across Four Sides

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{d 4}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Go Circumradius of Decagon given Diagonal across Three Sides

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{2 \cdot d 3}{\sqrt{14 + (6 \cdot \sqrt{5})}}

How to Evaluate Circumradius of Decagon given Height?

Circumradius of Decagon given Height evaluator uses Circumradius of Decagon = (1+sqrt(5))/2*Height of Decagon/sqrt(5+(2*sqrt(5))) to evaluate the Circumradius of Decagon, The Circumradius of Decagon given Height formula is defined as a line connecting the circumcenter of the circle that touches all vertices of the Decagon and any point on the circle, calculated using its height. Circumradius of Decagon is denoted by r_c symbol.

How to evaluate Circumradius of Decagon given Height using this online evaluator? To use this online evaluator for Circumradius of Decagon given Height, enter Height of Decagon (h) and hit the calculate button.

FAQs on Circumradius of Decagon given Height

What is the formula to find Circumradius of Decagon given Height?

The formula of Circumradius of Decagon given Height is expressed as Circumradius of Decagon = (1+sqrt(5))/2*Height of Decagon/sqrt(5+(2*sqrt(5))). Here is an example- 16.29766 = (1+sqrt(5))/2*31/sqrt(5+(2*sqrt(5))).

How to calculate Circumradius of Decagon given Height?

With Height of Decagon (h) we can find Circumradius of Decagon given Height using the formula - Circumradius of Decagon = (1+sqrt(5))/2*Height of Decagon/sqrt(5+(2*sqrt(5))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Circumradius of Decagon?

Here are the different ways to Calculate Circumradius of Decagon-

Circumradius of Decagon=Width of Decagon/2
Circumradius of Decagon=Diagonal across Five Sides of Decagon/2
Circumradius of Decagon=(1+sqrt(5))/2*Diagonal across Four Sides of Decagon/sqrt(5+(2*sqrt(5)))

Can the Circumradius of Decagon given Height be negative?

No, the Circumradius of Decagon given Height, measured in Length cannot be negative.

Which unit is used to measure Circumradius of Decagon given Height?

Circumradius of Decagon given Height is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Circumradius of Decagon given Height can be measured.

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